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arXiv · 1506.00141

A free boundary problem arising in PDE optimization

Giuseppe Buttazzo·Edouard Oudet·Bozhidar Velichkov
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Abstract

A free boundary problem arising from the optimal reinforcement of a membrane or from the reduction of traffic congestion is considered; it is of the form $$\sup_{\int_D\theta\,dx=m}\ \inf_{u\in H^1_0(D)}\int_D\Big(\frac{1+\theta}{2}|\nabla u|^2-fu\Big)\,dx.$$ We prove the existence of an optimal reinforcement $\theta$ and that it has some higher integrability properties. We also provide some numerical computations for $\theta$ and $u$.

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Giuseppe Buttazzo, Edouard Oudet, Bozhidar Velichkov. 2015-05-30. A free boundary problem arising in PDE optimization. https://arxiv.org/abs/1506.00141

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